Problem: What do the following two equations represent? $-5x+4y = 3$ $-8x-10y = 3$
Putting the first equation in $y = mx + b$ form gives: $-5x+4y = 3$ $4y = 5x+3$ $y = \dfrac{5}{4}x + \dfrac{3}{4}$ Putting the second equation in $y = mx + b$ form gives: $-8x-10y = 3$ $-10y = 8x+3$ $y = -\dfrac{4}{5}x - \dfrac{3}{10}$ The slopes are negative inverses of each other, so the lines are perpendicular.